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\title{{\large Computer Graphics} II\\A nice looking Billiard Simulation\\{\large Proposal}}
\author{Klaus Becker, Peter Kling, Christian Wolf}
\date{\today}

\begin{document}

\maketitle

\begin{abstract}
This document will give a short overview over our project for the course \emph{Computer Graphics II} held by Prof. Dr. Gitta Domik in the summer term 2008. We will present the idea including its motivation as well as the techniques we are planning to use.
\end{abstract}

\tableofcontents

\newpage

\section{Project idea}

This section gives a short overview about our project. The guidelines for the project can be found in the lecture material \cite{ref:cgii}. In summary we have to design, develop and present a graphical demo that gives a small overview about the topics we discussed in the lecture.

\subsection{Motivation}

Although the main focus of the project lies self--evidently in the graphical part, we decided not only to create a graphical demo but also to bring in some more advances features. We want to introduce some kind of interaction in such a way, that the observer has the possibility to interact with the scene. So, the main criteria our project is designed for are:

\begin{itemize}
\item possibility to include several graphical effects like textures, bump--map\-ping, reflections, lighting/shadows, $\ldots$
\item interactive scene (not only animation)
\item scalability (i.e. let enough room to include more effects or to omit/change some minor aspects during development)
\end{itemize} 


\subsection{Project description}

We decided to design a scene build around a billiard table. Billiard enables us to include some kind of --- not too complex --- physics to cover the interactive aspect. The first milestone will be the modelling of the billiard table and the balls, together with a first version of a \emph{specialised physic engine}.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.7\linewidth]{./pictures/billiardTable}
\end{center}
\end{figure}

Already here we have many possibilities to integrate different graphical effects like \emph{bump--mapping} for the cloth of the billiard table or \emph{environment mapping} for highly reflective billiard balls. Furthermore, we can extend the scene by more objects like table lamps (for \emph{dynamic shadows}) or some kind of ``smoking'' objects like cigars.

\section{Techniques we are planning to use}

This section lists the techniques we are planning to use for the different aspects of our scene as well as a short explanation of the physic engine.

\subsection{Graphical techniques}
\begin{itemize}
\item \textbf{Textures:} for balls, table, $\ldots$
\item \textbf{Bump Mapping:} mainly for the cloth texture of the billiard table
\item \textbf{Shadows:} probably via shadow mapping or shadow volumes (see \cite{ref:shadows})
\item \textbf{Particle Engine:} for drift smoke
\item \textbf{Lighting Effects:} specular lighting, reflections, $\ldots$
\item \textbf{Object Modelling:} billiard table, balls, lamps, $\ldots$
\end{itemize}


\subsection{Physical model}

In our physical model we consider friction, momentum and collisions between several balls and the table. By using physical laws we try to provide a fairly realistic model for the movement of the billiard balls. The most important laws we are going to use are the \emph{conservation of momentum} and several rules about the movement of rigid bodies\footnote{Most of which are subject material in school.}. As an example consider figure \ref{fig:ballCollision}, where we depicted the conservation of momentum in the collision of two balls of equal mass (but different size).

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=\linewidth]{./pictures/ballCollision}
\caption{Conservation of momentum between two balls of the same mass but different size. The arrows indicate the velocity vectors, which do --- except for a factor --- correspond to the momenta (because of the equality of the masses).} \label{fig:ballCollision}
\end{center}
\end{figure}


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% references
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\begin{thebibliography}{9.}
\bibitem{ref:cgii}
\newblock \href{http://www.cs.upb.de/fachgebiete/ag-domik/lehre/vorlesungen/ss08-computer-graphics-ii.html}{{C}omputer {G}raphics {II}}, summer term 2008, University of Paderborn

\bibitem{ref:shadows}
\newblock
\href{http://en.wikipedia.org/wiki/Shadow_mapping}{Wikipedia article: shadow mapping}, April 2008\\
\href{http://en.wikipedia.org/wiki/Shadow_volume}{Wikipedia article: shadow volumes}, April 2008
\end{thebibliography}

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